The equilibrium conformations of isolated comb copolymer ring molecules in an athermal solution are investigated by off-lattice Monte Carlo simulations. The molecules considered consist of a closed flexible backbone densely grafted with flexible or rigid side chains. The study focuses on the influence of the length of the side chains on the conformational behavior. As a function of the side chain length the structure gradually stiffens until the size of the side chains approaches the diameter of the ring. Longer side chains do not influence the backbone conformation any further. The results are compared with the large body of knowledge available for linear cylindrical comb copolymer brushes.